Resumen de Fibered microstructures for some nonlocal Dirichlet forms

Marc Briane , Nicoletta Tchou

• In this article we study the homogenization of some fibered microstructures in order to obtain prescribed nonlocal effects from strongly local conduction problems in a bounded open set S2 of R . According to the Beurling-Deny formula these nonlocal effects are represented by a so-called jumping measure defined on the product Q x Q. In particular we reach the measures of type j (dx, dy) = IE (dy) where E is a smooth open subset of Q. If the set E is connected the starting microstructure is only composed of high conductivity fibers. If the set E is not connected we also need a mixture of high and low conductivity fibers in the regions separating the components of E.